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/* Floating-point remainder function.
Copyright (C) 2023 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<https://www.gnu.org/licenses/>. */
#include <libm-alias-double.h>
#include <libm-alias-finite.h>
#include <math-svid-compat.h>
#include <math.h>
#include "math_config.h"
/* With x = mx * 2^ex and y = my * 2^ey (mx, my, ex, ey being integers), the
simplest implementation is:
mx * 2^ex == 2 * mx * 2^(ex - 1)
or
while (ex > ey)
{
mx *= 2;
--ex;
mx %= my;
}
With the mathematical equivalence of:
r == x % y == (x % (N * y)) % y
And with mx/my being mantissa of a double floating point number (which uses
less bits than the storage type), on each step the argument reduction can
be improved by 11 (which is the size of uint64_t minus MANTISSA_WIDTH plus
the implicit one bit):
mx * 2^ex == 2^11 * mx * 2^(ex - 11)
or
while (ex > ey)
{
mx << 11;
ex -= 11;
mx %= my;
}
Special cases:
- If x or y is a NaN, a NaN is returned.
- If x is an infinity, or y is zero, a NaN is returned and EDOM is set.
- If x is +0/-0, and y is not zero, +0/-0 is returned. */
double
__fmod (double x, double y)
{
uint64_t hx = asuint64 (x);
uint64_t hy = asuint64 (y);
uint64_t sx = hx & SIGN_MASK;
/* Get |x| and |y|. */
hx ^= sx;
hy &= ~SIGN_MASK;
/* If x < y, return x (unless y is a NaN). */
if (__glibc_likely (hx < hy))
{
/* If y is a NaN, return a NaN. */
if (__glibc_unlikely (hy > EXPONENT_MASK))
return x * y;
return x;
}
int ex = hx >> MANTISSA_WIDTH;
int ey = hy >> MANTISSA_WIDTH;
int exp_diff = ex - ey;
/* Common case where exponents are close: |x/y| < 2^12, x not inf/NaN
and |x%y| not denormal. */
if (__glibc_likely (ey < (EXPONENT_MASK >> MANTISSA_WIDTH) - EXPONENT_WIDTH
&& ey > MANTISSA_WIDTH
&& exp_diff <= EXPONENT_WIDTH))
{
uint64_t mx = (hx << EXPONENT_WIDTH) | SIGN_MASK;
uint64_t my = (hy << EXPONENT_WIDTH) | SIGN_MASK;
mx %= (my >> exp_diff);
if (__glibc_unlikely (mx == 0))
return asdouble (sx);
int shift = clz_uint64 (mx);
ex -= shift + 1;
mx <<= shift;
mx = sx | (mx >> EXPONENT_WIDTH);
return asdouble (mx + ((uint64_t)ex << MANTISSA_WIDTH));
}
if (__glibc_unlikely (hy == 0 || hx >= EXPONENT_MASK))
{
/* If x is a NaN, return a NaN. */
if (hx > EXPONENT_MASK)
return x * y;
/* If x is an infinity or y is zero, return a NaN and set EDOM. */
return __math_edom ((x * y) / (x * y));
}
/* Special case, both x and y are denormal. */
if (__glibc_unlikely (ex == 0))
return asdouble (sx | hx % hy);
/* Extract normalized mantissas - hx is not denormal and hy != 0. */
uint64_t mx = get_mantissa (hx) | (MANTISSA_MASK + 1);
uint64_t my = get_mantissa (hy) | (MANTISSA_MASK + 1);
int lead_zeros_my = EXPONENT_WIDTH;
ey--;
/* Special case for denormal y. */
if (__glibc_unlikely (ey < 0))
{
my = hy;
ey = 0;
exp_diff--;
lead_zeros_my = clz_uint64 (my);
}
int tail_zeros_my = ctz_uint64 (my);
int sides_zeroes = lead_zeros_my + tail_zeros_my;
int right_shift = exp_diff < tail_zeros_my ? exp_diff : tail_zeros_my;
my >>= right_shift;
exp_diff -= right_shift;
ey += right_shift;
int left_shift = exp_diff < EXPONENT_WIDTH ? exp_diff : EXPONENT_WIDTH;
mx <<= left_shift;
exp_diff -= left_shift;
mx %= my;
if (__glibc_unlikely (mx == 0))
return asdouble (sx);
if (exp_diff == 0)
return make_double (mx, ey, sx);
/* Multiplication with the inverse is faster than repeated modulo. */
uint64_t inv_hy = UINT64_MAX / my;
while (exp_diff > sides_zeroes) {
exp_diff -= sides_zeroes;
uint64_t hd = (mx * inv_hy) >> (BIT_WIDTH - sides_zeroes);
mx <<= sides_zeroes;
mx -= hd * my;
while (__glibc_unlikely (mx > my))
mx -= my;
}
uint64_t hd = (mx * inv_hy) >> (BIT_WIDTH - exp_diff);
mx <<= exp_diff;
mx -= hd * my;
while (__glibc_unlikely (mx > my))
mx -= my;
return make_double (mx, ey, sx);
}
strong_alias (__fmod, __ieee754_fmod)
libm_alias_finite (__ieee754_fmod, __fmod)
#if LIBM_SVID_COMPAT
versioned_symbol (libm, __fmod, fmod, GLIBC_2_38);
libm_alias_double_other (__fmod, fmod)
#else
libm_alias_double (__fmod, fmod)
#endif
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